This invention relates to a method and apparatus for the measurement of surface heat transfer, i.e. the rate of heat flow per unit area into or out of a surface. This type of measurement is of value in energy production and utilization systems of many kinds. The existing methods for performing such measurements employ three techniques: (1) measurement of an applied power; (2) measurement of a change in temperature; or (3) measurement of a temperature difference.
The first technique for measuring surface heat transfer is limited in accuracy, particularly for measurements over a small surface area. This limitation is described in my research paper, "Analysis and Design of Experimental Systems for Heat Transfer Measurement from Constant Temperature Surfaces," co-authored by T. VandenBerghe and submitted for publication to the International Journal of Heat and Mass Transfer. Other approaches to the measurement of surface heat transfer which employ measurements of applied power are described in: "An Instrument for the Measurement of Heat Flux from a Surface with Uniform Temperature," by Kraabel, J. S., Baughn, J. W. and McKillop, A. A., published in ASME Journal of Heat Transfer, Vol. 102, 1980, pp. 576-578; "Total and Local Heat Transfer from a Smooth Circular Cylinder in Cross-Flow at High Reynolds Number," by Achenbach, E., published in International Journal of Heat and Mass Transfer, Vol. 18, 1975, pp. 1387-1396; and "Design and Calibration of a Local Heat-Flux Measurement System for Unsteady Flows," by Campbell, D. S., Gunduppa, M., and Diller, T. E., published in Fundamentals of Forced and Mixed Convection, ASME 1985, pp. 73-80. These references illustrate the difficulty of performing surface heat transfer measurements by measurement of applied power.
The second technique for surface heat transfer measurement is described by Gladden, H. J. and Proctor, M. P. in "Transient Technique for Measuring Heat Transfer Coefficients on Stator Airfoils in a Jet Engine Environment", AIAA Paper No. 85-1471, July 1985, and by Elrod, W. C., Gochenaur, J. E., Hitchcock, J. E., and Rivir, R. B., in "Investigation of Transient Techniques for Turbine Vane Heat Transfer Using a Shock Tube," ASME Paper 85-IGT-17, 1985. While this technique is easier to apply to a local region of a surface than the first method, the results are a function of both the surface material properties and the analytical model used to reduce the data. If the temperature measurements are made in the material of the surface itself, they may be limited in range or accuracy because the material is hard to form or machine into the required configuration. Calibrations in situ of transient heat flux gages are usually quite difficult.
A device which employs the third technique for surface heat transfer measurement is described in U.S. Pat. No. 3,607,445, issued to Frank F. Hines. This device is a heat flux gage comprising a planar thermal resistance element and a differential thermopile whose "cold" junctions are on one face of the planar thermal resistance element, and whose "hot" junctions are on the other. The heat transfer of a surface is measured with this device by placing the planar thermal resistance element in close thermal contact with the surface, and using the output voltage of the thermopile to measure the temperature difference across the planar thermal resistance element. This gage must be calibrated to determine its voltage output as a function of heat transfer; a value affected by the thickness and material of the planar thermal resistance element, the number of thermopile elements, and the materials and configuration of the thermoelectric junctions. While the Hines gage and others using similar principles are effective and accurate, they have a number of known disadvantages.
The output voltage of the Hines gage is proportional to the temperature drop across the planar thermal resistance element. For convenient and precise measurement of this voltage it would be desirable to make the planar thermal resistance element as thick as possible, and fabricate it from a material with high thermal resistivity. However, in many experiments the gage must be physically thin (e.g. in aerodynamics, to minimize surface flow disturbances), and the temperature drop across the gage must be a minimum to avoid disrupting the heat flux distribution over the surface. Increasing the number of thermopile elements to obtain a larger voltage for a desirably thin planar thermal resistance element will increase the surface area of the gage, and render it less useful for detailed measurements of thermal flux distribution.
The application of such gages to surfaces whose materials may be ceramic, metallic, or composite, and whose shape may be flat or curved, is a challenge to the experimenter. They may be attached by use of an adhesive, but the thermal and mechanical properties of the adhesive are then critical to the accuracy of heat flux measurement. The temperature drop across the adhesive layer is usually a significant part of the total drop across the gage, and the maximum service temperature of the gage itself is equal to that of the adhesive.
In his report on Calspan Field Services, Inc. AEDC Project D228VW, "A Durable, Intermediate Temperature, Direct Reading Heat Flux Transducer for Measurements in Continuous Wind Tunnels", AEDC TR-81-19, November, 1981, page 10, the author C. T. Kidd summarizes the dilemma facing users of heat flux gages by saying
"An ideal transducer for aerodynamic heat transfer measurement applications in continuous wind tunnels would have an output signal directly proportional to the heat flux incident on the sensing surface, a heat flux sensitivity .ltoreq.20 mv/Btu/ft.sup.2 -sec, and a time response on the order of 0.10 sec. In addition, the ideal transducer would have a sensing surface temperature exactly the same as the adjacent model or test article surface, a maximum continuous service temperature of at least 1,500.degree. F., and a calibration scale factor completely independent of ambient gage temperature. Physical characteristics of the transducer should include small size (&gt;0.125 in. diam. by .ltoreq.0.35 in.), ability to be contoured exactly to match a model surface, and ability to withstand any normal test environment with no structural damage. It may be possible to achieve one or more of these ideal performance factors with practical application of the Schmidt-Boelter concept; however, even an inexperienced gage designer would recognize that it would be virtually impossible to attain all of these performance factors in one gage. Therefore, design tradeoffs have to be made."
In his definition of the "ideal transducer", the author was mainly concerned with applications in which the heat flux is so low that it is difficult to measure the thermoelectric output potential of a gage. A more challenging case is one where the heat flux is high, and the gage output is no longer a linear function of heat flux because the temperature drop across the gage is large. For this case the "ideal transducer" is a gage with a lower heat flux sensitivity, but having an output potential more nearly linear with heat flux at higher values.
We have developed a heat flux gage which employs a novel construction and method of application to a surface, thereby solving the problems of previous devices and yielding characteristics which surpass the ideal of Kidd, as it would apply to high heat flux applications. The details of construction and application of this gage are hereinafter described, along with its features and advantages in the measurement of heat flux under a variety of circumstances.